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42                        ANALYTICAL MECHANICS
52. Transmissibility of Force.  A force which acts upon a rigid body may be considered to be applied to any particle of the body which lies on the line of act ion of (ho force. I n order to prove this statement consider the rigid body A, Fig. 32, which is in equilibrium under the action of the two
equal and opposite forces F and -F. Now suppose we change the point of application of F, without elwngiiiK either its direction or its line of application. Evidently the equilibrium is not disturbed, because by moving F in its line of action we neither changed the sum of the forces nor the sum of their moments about any axis. Therefore the line of action of a force is of importance* and not its point of application.
53. Internal Forces.  Internal forces do not a/cct (he <v/w-librium of a rigid body. This is a direct consequence of the law of "action and reaction." Since by definition the internal forces are due to the interact ion bet ween I he part ides of the system these forces exist in equal and opposite pairs, therefore mutually annul cadi other.
ILLUSTRATIVE EXAMPLES,
1. A uniform beam rests with its lower end on Hinootlt horizontal ground and its upper end against a smooth vertical wall. The beam in held from slipping by means of a string which connects the foot of tlm beam with the foot of the wall. Find the tensile, force in the wiring ancl the reactions at the ends of the beam.
There are four forces acting upon the beam, i.e., the two rear!ions, Ri and R2, the tensile force T and the weight W. Since both the grouiul nnd the wall are supposed to be smooth, Rt is normal to the ground, arid R3